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10. Calculate the no-arbitrage forward price for a 100-day forward on a stock that is currently priced at $30.00 and is expected to pay a dividend of $0.40 in 15 days, $0.40 in 85 days, and $0.50 in 175 days. The annual risk-free rate is 5%, and the yield curve is flat.

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Answer #1

As the dividend figures are expressed in terms of fixed numbers and not as percentages, compounding can be assumed to be distinct and not continuous in nature. Further, only the first two dividends impact the forward contract's price as the last dividend comes in only after expiry of the forward contract.

Current Price = $ 30, Annual Risk Free Rate = 5%

The stock receives a dividend of $ 0,4 after 15 days and another $ 0.4 after 85 days

Total Present Value of these dividends = 0.4 / [1 + 0.05 x (15/365)] + 0.4 / [1+ 0.05 x (85/365)] = $ 0.3992 + 0.3954 = $ 0.7946

Therefore, Forward Contract Price = (30 - 0.7946) x [1+0.05 x (100/365)] = $ 29.60547 ~ $ 29.61

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